Write the equation of a line that is perpendicular to $y=0.25x-7$ and that passes through the point $(-6,8)$.
Getting started Key idea: The slopes of perpendicular lines are negative reciprocals of each other. Step 1: Find the slope Slope of the given line: ${0.25=\dfrac{1}{4}}$ So, the slope of the perpendicular line: $C{-4}$ Step 2: Substitute the known point into linear equation The perpendicular line will have a slope of $C{-4}$ and pass through the point ${(-6,8)}$. Let's start from the point-slope form of the equation of the perpendicular line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{8} &= C{-4}(x-{(-6)})\\\\\\ y-8 &= C{-4}x -24 \\\\\\ y &= C{-4}x { -16} \end{aligned}$ Answer $y=C{-4}x {-16}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ $y$ $x$